A SIMPLE WAY TO ASSESS THE SPECTRAL LINES INFORMATIVITY OF A CHI-SQUARE MOLECULE IN ANALYZING SMALL SAMPLES OF BIOMETRIC DATA

DOI: 10.5937/jaes16-18435

This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.

Volume 16 article 546 pages: 404 - 409

The
prerequisites for reducing the test sample chi-square Pearson test size from
400 to 32 or fewer examples while maintaining its power are considered. The
urgency of the problem results from the fact that when learning and testing the
biometric identification means to identify the personality, it is not possible
to use large volumes of learning and test samples. The conditions under which
the chi-square test on small samples from the continuous distribution of values
becomes a discrete distribution of values are formalized. Normal and uniform
laws of values distribution use histograms with uniform intervals, which
accurately relate the central intervals of the histogram to the mathematical
expectation calculated on the test sample. 16 experiments shown that the
chi-square-synchronized test built on histograms with four equal intervals has
a discrete probability spectrum consisting of only 20 significant spectral
lines. A simple method for estimating the informativity of each of the
important spectral components is proposed. Traditional statistical assessments
can be strengthened by the following deeper level of the spectral components
analysis of small samples of biometric data. The second deeper level of
statistical processing should be substantially more powerful. Under the same
conditions, the computational informativity increases from 2.22 bits to 24.95
bits due to the transition from simple continual calculations to discrete
calculations of high computational complexity.

Volchikhin, V.I.,
Ivanov, A.I., Funtikov, V.A. (2005). Fast learning algorithms for neural
network mechanisms of biometric-cryptographic information protection.
Publishing House of the Penza State University, Penza.

Malygin, A.Yu.,
Volchikhin, V.I., Ivanov, A.I., Funtikov, V.A. (2006). Fast testing algorithms
for neural network mechanisms of biometric-cryptographic information
protection. Publishing House of the Penza State University, Penza.

Yazov, Yu.K. (2012).
Neural network protection of personal biometric data. Radio Engineering, Moscow.

Federal Agency on
Technical Regulating and Metrology. (2001). R 50.1.037-2002. Recommendations
on standardization. Applied statistics. Rules for verifying the agreement
between the experimental and the theoretical distributions. Part I. x2 type criteria.

Serikova, N.I.,
Ivanov, A.I., Kachalin, S.V. (2014). Biometric stats: smoothing histograms
based on small training sample. Scientific Journal of Science and Technology,
vol. 3, no. 55, 146-150.

Serikova, N.I.
(2015). Assessment of the likelihood of the normal distribution hypothesis by
the Gini criterion for smoothed histograms constructed on small test samples.
Questions of Radio Electronics, vol. 1, 85-94.

Ivanov, A.I.,
Akhmetov, B.B., Serikova, Yu.I. (2016). Strengthening the power of the
chi-square test with tenfold increase in freedoms of statistical computations
on small test samples. Reliability and Quality of Complex Systems, vol. 4, no.
16, 121-127. DOI: 10.21685/2307-4205-2016-4-17

Akhmetov, B.B.,
Ivanov, A.I. (2016). Multidimensional statistics of essentially dependent
biometric data generated by neural network emulators of quadratic forms. LEM,
Almaty.

Akhmetov, B.B.,
Ivanov, A.I., Serikova, N.I., Funtikova, Yu.V. (2015). The discrete nature of
the chi-square test distribution for small test samples. Bulletin of the
National Academy of Sciences of the Republic of Kazakhstan, vol. 1, no. 353,
17-25.

Kulagin, V.P.,
Ivanov, A.I., Gazin, A.I., Akhmetov, B.B. (2016). Cyclic continuum-quantum
computing: Strengthening the Chi-Square test power on small samples. Analytics,
vol. 30, no. 5, 22-29.

Volchikhin, V.I.,
Ivanov, A.I., Serikov, A.V., Serikova, Yu.I. (2017). Quantum superposition of
the state discrete spectrum of mathematical correlation molecule for small
samples of biometric data. Mordovia University Bulletin, vol. 27, no. 2,
224-238. DOI: 10.15507/0236-2910.027.201702.224-238

Volchikhin, V.I.,
Ivanov, A.I. (2017). Neural Network Molecule: a Solution of the Inverse
Biometry Problem through Software Support of Quantum Superposition on Outputs
of the Network of Artificial Neurons. Mordovia University Bulletin, vol. 27,
no. 4, 518-529. DOI: 10.15507/0236-2910.027.201704.518-529

Volchikhin, V.I.,
Ivanov, A.I., Gazin, A.I., Bannih, A.G. (2017). Conditions of obtaining the
discrete kurtosis spectrum of statistical distributions of biometric data for
small samples. Journal of Computational and Engineering Mathematics, vol. 4,
no. 4, 53-63. DOI: 10.14529/jcem170405

Nilson, M., Chang,
I. (2006). Quantum calculations and quantum information. Mir Publishers,
Moscow.

Filippov, V.V.,
Mitsuk, S.V. (2017). Modelling magnetoresistance effect in limited anisotropic
semiconductors. Chinese Physics Letters, vol. 34, no. 7, 077201. DOI:
10.1088/0256-307X/34/7/077201

Stepanov, N.F.
(2001). Quantum mechanics and quantum chemistry. Mir Publishers, Moscow.

State Standard R
52633.5-2011. (2011). Data Protection. Information Protection Technique.
Automatic Learning Neural Network Converters Biometry-Code Access.
Standartinform, Moscow.

Ivanov, A.I. (2016).
Multidimensional neural network processing of biometric data with software
reproduction of quantum superposition effects. Penza Scientific and Research
Electronic Technical Institute, Penza